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In general relativity, gravity is described as a distortion of space time. Most vulgarized books use the simplified image of a 2D plane being bent downwards by a mass, so that any matter traveling in the area would have to follow the bending of the plane, which would then explain why things are attracted to one another.

Keeping the same simplified metaphor, could we imagine something that would
bend the plane upwards, thus causing objects to be repelled? Would such a thing be considered to have negative mass? Is the concept theoretically possible?

Asked By: Thomas G. from Belgium

The best answer to this would probably be that “negative mass” has never been
observed in Nature. I’m not aware of anything that specifically prohibits it; it has simply
never been observed. (Incidentally, antimatter has positive mass, just like ordinary
matter.)

It’s interesting to see what happens if you make mass negative in the existing laws
of physics. For example: suppose you have two planets near each other, each of which
has a negative mass. Would they attract or repel? The answer is: using Newton’s law of
gravity, the force between two negative masses would be the same as if they were two
positive masses, and the two planets would experience an attractive force.

However, by
Newton’s second law (F = ma), if mass is negative, then force and acceleration are
in opposite directions, so the two planets of negative mass, although experiencing an
attractive force, would accelerate away from each other.

Now suppose you had a -1 kg negative mass, held it up above the ground (on
Earth), and dropped it. What would happen? The answer is: it would fall just like
any other mass.

Since the Earth’s mass is positive and the -1 kg mass is negative,
there will be a repulsive force acting on the mass. But because of Newton’s second
law, a repulsive force acting upward on a negative mass would cause it to accelerate
downward.

Another way to look at this is that the acceleration of any object due to the Earth’s gravity is 9.8 m/s2 downward, regardless of the mass of the object — even if
its mass is negative.

Something especially interesting happens if you make a “mass dipole”: a positive
mass and a negative mass of equal magnitude placed out in space and separated by a
fixed distance. Let’s imagine, for example, two such masses, with the negative mass
on the left and the positive mass on the right.

By Newton’s law of gravity, the force
between the two masses will be repulsive. A repulsive force acting on the negative
mass acts to the left, but by Newton’s second law it will accelerate in the opposite
direction (to the right). A repulsive force acting on the positive mass will cause it to
accelerate in the same direction (also to the right).

So this hypothetical “mass dipole”
will apparently spontaneously accelerate to the right, its speed increasing indefinitely,
with the positive mass leading and the negative mass trailing. The conservation of
energy would not be violated, since the total mass of the system is zero, so its kinetic
energy is also always zero, regardless of the speed of the mass dipole.

Of course, this is all just fanciful playing with the physics equations, seeing what
would happen if mass were made negative. In real life, no negative mass has ever
been observed. If negative mass were to exist, we don’t know how the laws of physics
would have to be modified to accommodate it.

For example, our present understanding
of physics includes something called the “equivalence principle” which states that
gravitational mass (as it appears in Newton’s law of gravity) is exactly equal to inertial
mass (as it appears in Newton’s second law). If negative mass were discovered, we
might find that the equivalence principle does not hold for negative mass. Unless we
were to observe some negative mass in Nature, we just don’t know how the laws of
physics might change.